×

Adaptive control with guaranteed transient and steady state tracking error bounds for strict feedback systems. (English) Zbl 1158.93325

Summary: Two robust adaptive control schemes for single-input single-output strict feedback nonlinear systems possessing unknown nonlinearities, capable of guaranteeing prescribed performance bounds are presented in this paper. The first assumes knowledge of only the signs of the virtual control coefficients, while in the second we relax this assumption by incorporating Nussbaum-type gains, decoupled backstepping and non-integral-type Lyapunov functions. By prescribed performance bounds we mean that the tracking error should converge to an arbitrarily predefined small residual set, with convergence rate no less than a prespecified value, exhibiting a maximum overshoot less than a sufficiently small prespecified constant. A novel output error transformation is introduced to transform the original “constrained” (in the sense of the output error restrictions) system into an equivalent “unconstrained” one. It is proven that the stabilization of the “unconstrained” system is sufficient to solve the problem. Both controllers are smooth and successfully overcome the loss of controllability issue. The fact that we are only concerned with the stabilization of the “unconstrained” system, severely reduces the complexity of selecting both the control parameters and the regressors in the neural approximators. Simulation studies clarify and verify the approach.

MSC:

93B35 Sensitivity (robustness)
93C40 Adaptive control/observation systems
92B20 Neural networks for/in biological studies, artificial life and related topics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Chen, D.; Yang, J., Implementable adaptive backstepping neural control of uncertain strict-feedback nonlinear systems, Advances in Neural Networks, 3972, 875-880 (2006)
[2] Ding, Z.; Ye, X., A flat-zone modification for robust adaptive control of nonlinear output feedback systems with unknown high-frequency gains, IEEE Transactions on Automatic Control, 47, 2, 358-363 (2002) · Zbl 1364.93699
[3] Ge, S. S.; Hong, F.; Lee, T. H., Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients, IEEE Transactions on Systems, Man, and Cybernetics—Part B: Cybernetics, 34, 1, 499-516 (2004)
[4] Ge, S. S.; Wang, C., Direct adaptive control of a class of nonlinear systems, IEEE Transactions on Neural Networks, 13, 1, 214-221 (2002)
[5] Ge, S. S.; Wang, J., Robust adaptive neural control for a class of perturbed strict feedback nonlinear systems, IEEE Transactions on Neural Networks, 13, 6, 1409-1419 (2002)
[6] Ge, S. S.; Wang, J., Robust adaptive tracking for time-varying uncertain nonlinear systems with unknown control coefficients, IEEE Transactions on Automatic Control, 48, 8, 1463-1469 (2003) · Zbl 1364.93704
[7] Gupta, M. M.; Rao, D. H., Neuro-control systems: Theory and applications (1994), New York: IEEE
[8] Lewis, F. L.; Jagannathan, S.; Yesildirek, A., Neural network control of robot manipulator and nonlinear systems (1999), Taylor and Francis: Taylor and Francis London
[9] Miller, D. E.; Davison, E. J., An adaptive controller which provides arbitrarily good transient and steady state response, IEEE Transactions on Automatic Control, 36, 1, 68-81 (1991) · Zbl 0725.93074
[10] Polycarpou, M. M.; Mears, M. J., Stable adaptive tracking of uncertain systems using nonlinearly parameterized on-line approximators, International Journal of Control, 70, 3, 363-384 (1998) · Zbl 0945.93563
[11] Rovithakis, G. A., Stable adaptive neuro-control design via lyapunov function derivative estimation, Automatica, 37, 8, 1213-1221 (2001) · Zbl 0988.93038
[12] Rovithakis, G. A.; Christodoulou, M. A., Adaptive control with recurrent high-order neural networks (2000), London: Springer
[13] Spooner, J. T.; Maggiore, M.; Ordonez, R.; Passino, K. M., Stable adaptive control and estimation for nonlinear systems-neural and fuzzy approximator techniques (2002), Wiley: Wiley New York
[14] Wang, C.; Hill, D. J.; Ge, S. S.; Chen, G., An ISS-modular approach for adaptive neural control of pure-feedback systems, Automatica, 42, 5, 723-731 (2006) · Zbl 1137.93367
[15] Xu, H.; Ioannou, P. A., Robust adaptive control for a class of MIMO nonlinear systems with guaranteed error bounds, IEEE Transactions on Automatic Control, 48, 5, 728-742 (2003) · Zbl 1364.93228
[16] Yan, L.; Hsu, L.; Xiuxia, S., A variable structure MRAC with expected transient and steady state performance, Automatica, 42, 5, 805-813 (2006) · Zbl 1137.93015
[17] Ye, X., Asymptotic regulation of time-varying uncertain nonlinear systems with unknown control directions, Automatica, 35, 7, 929-935 (1999) · Zbl 0945.93542
[18] Ye, X.; Jingping, J., Adaptive nonlinear design without a priori knowledge of control directions, IEEE Transactions on Automatic Control, 43, 11, 1617-1621 (1998) · Zbl 0957.93048
[19] Zhang, T.; Ge, S. S.; Hang, C. C., Adaptive neural network control for strict-feedback nonlinear systems using backstepping design, Automatica, 36, 12, 1835-1846 (2000) · Zbl 0976.93046
[20] Zhou, J.; Wen, C.; Zhang, Y., Adaptive backstepping control of a class of uncertain nonlinear systems with unknown backlash-like hysteresis, IEEE Transactions on Automatic Control, 49, 10, 1751-1757 (2004) · Zbl 1365.93251
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.